Centrifugal gyroscopic devices, and associated systems and methods

This application is a continuation of U.S. patent application Ser. No. 18/301,178, filed on Apr. 14, 2023, and titled “CENTRIFUGAL GYROSCOPIC DEVICES, AND ASSOCIATED SYSTEMS AND METHODS,” which claims the benefit of U.S. Provisional Patent Application No. 63/332,196, filed on Apr. 18, 2022, and titled “CENTRIFUGAL GYROSCOPIC DEVICES, AND ASSOCIATED SYSTEMS AND METHODS,” each of which are incorporated herein by reference in its entirety.

The present technology is directed to centrifugal gyroscopic devices for generating power and/or efficiently summing energy, and associated systems and methods.

U.S. Pat. No. 5,457,993, titled “Pendulous Oscillating Gyroscopic Accelerometer,” describes a pendulous oscillating gyroscopic accelerometer. The accelerometer utilizes the principle that a gyroscopic torque is generated when an oscillating gyroscope is oscillated about a transverse axis. When the gyroscopic torque is balanced by a pendulous torque, a measurement of acceleration is provided. If the accelerometer is attached to the earth, gravity is measured. As such, the accelerometer operates as a sensing device.

Aspects of the present disclosure are directed generally toward centrifugal gyroscopic devices for generating power and/or efficiently summing energy, and associated systems and methods. In several of the embodiments described below, a representative centrifugal gyroscopic device includes (i) a shaft, (ii) an arm coupled to the shaft, (iii) at least one rotor coupled to the arm, and (iv) a control system operably coupled to at least one of the shaft, the arm, and the rotor. The shaft is rotatable about a first axis and the arm is configured to rotate with the shaft. The arm is pivotable about a second axis different from the first axis, and the at least one rotor is configured to pivot with the arm about the second axis. The at least one rotor is further pivotable about a third axis different from the first and second axes. The control system is configured to bring the shaft, the arm, and the rotor into a resonant mode of operation in which (a) the shaft rotates at a rotational rate, (b) the arm oscillates about the second axis at a first frequency generally equal to the rotational rate, and (c) the at least one rotor oscillates about the third axis at a second frequency generally equal to the first frequency. Energy can be input into the device via the control system to control the motion of the shaft, the arm, and the rotor; and energy can be output from the device via the shaft, such as via a power generator coupled to the shaft and configured to convert the mechanical energy from the rotation of the shaft into electrical energy.

During operation, the rotation of the shaft rotates the arm and generates a centrifugal force that acts against the arm to oscillate the arm about the second axis. The oscillating motion of the arm and the at least one rotor combine to generate a gyroscopic torque that acts to rotate the shaft about the first axis. In some embodiments, the control system is configured to change a phase relationship between the frequency of the oscillation of the arm about the second axis and the frequency of the oscillation of the at least one rotor about the third axis to change an average value of the gyroscopic torque. For example, the control system can drive the arm and/or the at least one rotor via one or more motor assemblies to bring the frequency of the oscillation of the arm about the second axis and the frequency of the oscillation of the at least one rotor about the third axis more into phase to increase the gyroscopic torque.

In some aspects of the present technology, it is expected that the net energy output from the device will exceed the net energy input into the device via the control system. In some aspects of the present technology, the device can provide an energy output that is more efficient than conventional motor assemblies-even if the energy output from the device is not greater than the energy input to the device. Specifically, the control system can include one or more relatively small motor assemblies configured to drive the shaft, the arm, and/or the rotors. The power input to each of the motor assemblies can be relatively small compared to the total power output of the device via the shaft. Such smaller motors can be relatively more efficient than a comparable motor assembly configured to directly rotate the shaft to achieve the same output power. Therefore, the arrangement of the device can advantageously allow for the power inputs from several smaller motor assemblies to drive a series of motions (e.g., oscillations and rotations) that efficiently combine to generate a relatively larger power output.

1 16 FIGS.-F Certain details are set forth in the following description and into provide a thorough understanding of various embodiments of the present technology. In other instances, well-known structures, materials, operations, and/or systems often associated with gyroscopes, oscillating and rotating systems, generators, motors, pivotable couplings, and the like, are not shown or described in detail in the following disclosure to avoid unnecessarily obscuring the description of the various embodiments of the technology. Those of ordinary skill in the art will recognize, however, that the present technology can be practiced without one or more of the details set forth herein, and/or with other structures, methods, components, and so forth. The terminology used below is to be interpreted in its broadest reasonable manner, even though it is being used in conjunction with a detailed description of certain examples of embodiments of the technology.

The accompanying Figures depict embodiments of the present technology and are not intended to limit its scope unless expressly indicated. The sizes of various depicted elements are not necessarily drawn to scale, and these various elements may be enlarged to improve legibility. Component details may be abstracted in the Figures to exclude details such as position of components and certain precise connections between such components when such details are unnecessary for a complete understanding of how to make and use the present technology. Many of the details, dimensions, angles and other features shown in the Figures are merely illustrative of particular embodiments of the disclosure. Accordingly, other embodiments can have other details, dimensions, angles and features without departing from the present technology. In addition, those of ordinary skill in the art will appreciate that further embodiments of the present technology can be practiced without several of the details described below.

To the extent any materials incorporated herein by reference conflict with the present disclosure, the present disclosure controls. The headings provided herein are for convenience only and should not be construed as limiting the subject matter disclosed.

1 1 FIGS.A andB 1 FIG.B 1 FIG.A 1 FIG.C 1 FIGS.A 1 FIG.C 100 100 100 100 100 102 104 106 104 108 106 104 120 108 100 104 102 109 104 1 2 1 1 are partially-schematic isometric views of a centrifugal gyroscopic device(“device”) configured in accordance with embodiments of the present technology. The view inis rotated by about 90 degrees relative to the view shown in.is a side-cross sectional view of the devicetake along a plane extending along a first axis Aand a second axis Aof the devicein accordance with embodiments of the present technology. Referring to-IC together, in the illustrated embodiment the deviceincludes a framecomprising (i) a plurality of legs(e.g., four legs), (ii) a lower supportcoupled to or integrally formed with the legs(e.g., upper portions thereof), and (iii) an upper supportrotatably coupled to the lower supportand the legsvia a first shaft(best seen in; e.g., a spindle, a drive shaft, an output shaft, and/or an elongate member). The upper supportis rotatable about the first axis A(e.g., a spindle axis, a vertical axis, and/or an output axis). In some embodiments, the devicecan be oriented such that the first axis Aextends generally parallel to a surrounding gravitational field. The legscan be fixedly secured (e.g., via one or more fasteners) to the ground, a floor, and/or another surface. In some embodiments, the framefurther includes a platesecured between the legs.

100 110 108 107 126 110 110 112 114 114 114 112 114 113 112 114 113 112 113 112 113 113 112 126 110 114 106 108 120 110 1 FIG.C 4 FIG. 2 2 1 3 2 a b a a b b a c a b In the illustrated embodiment, the devicefurther includes an arm assemblypivotably mounted to the upper supportwithin an openingtherein via a second shaft() extending along the second axis A. The arm assemblycan also be referred to as an arm, a torque-summing assembly, and/or the like. The arm assemblyincludes (i) a housingcontaining one or more motor assemblies as described in detail below with reference to, and (ii) a pair of rotors(which can also be referred to as masses; identified individually as a first rotorand a second rotor) pivotably mounted to the housing. More specifically, the first rotorcan be pivotably coupled to/at a first end portionof the housingand the second rotorcan be pivotably coupled to/at a second end portionof the housingopposite the first end portion. The housingfurther includes a central portionbetween the first and second end portions-that is pivotably coupled to the housingvia the second shaftsuch that the arm assemblyis pivotable about the second axis A(e.g., an arm axis, and/or a hinge axis) orthogonal to the first axis A. The rotorsare each independently pivotable about a third axis A(e.g., a rotor axis, and/or a momentum reference axis) orthogonal to the first axis Aj and the second axis Ain its reference state. In some embodiments, the lower supportand/or the upper supportcan be omitted and/or the first shaftcan be directly coupled to the arm assembly.

1 FIG.C 1 1 FIGS.A-C 1 FIG.A 1 1 FIGS.A-C 120 106 121 121 106 120 121 120 108 100 130 109 121 120 130 120 108 110 120 130 1 1 1 a b b a As best seen in, the first shaftextends through an interior of the lower supportalong the first axis Aand includes a lower end portionand an upper end portion. In some embodiments, the lower supportcan at least partially support the first shaftvia one or more bearings (not shown). The upper end portionof the first shaftis coupled to the upper support. Referring totogether, the deviceincludes a shaft motor assemblycoupled to the plateand operably coupled to the lower end portionof the first shaft. The shaft motor assemblycan include a motor (e.g., a rotary motor) and associated gearbox and is configured to drive the first shaftto rotate about the first axis Ain a clockwise and/or counterclockwise direction as indicated by arrow C into drive the upper supportand arm assemblyto rotate together about the first axis A. Although the first shaftis shown as spaced apart from the shaft motor assemblyinfor clarity, these components can be directly attached together and/or operably coupled together via an intervening structure such as a link, coupling, shaft, and/or the like.

100 122 120 122 123 120 124 123 120 122 120 122 130 120 In some embodiments, the devicecan further include a brake mechanismoperably coupled to the first shaft. The brake mechanismcan include a brake platefixed to the first shaftand a brake actuatorconfigured to selectively engage the brake plateto slow or stop a rotational rate of the first shaft. In some embodiments, the brake mechanismcan include other components for selectively slowing the rotational rate of the first shaft. In some embodiments, the brake mechanismcan be omitted and/or the shaft motor assemblycan be configured to brake/slow rotation of the first shaft.

100 132 132 132 108 110 110 132 126 127 132 127 132 132 126 110 110 132 132 100 132 132 a b a a b b 2 FIG. 1 2 FIGS.C and 1 FIG.C 1 2 FIGS.A and 2 2 1 2 2 1 2 1 1 In the illustrated embodiment, the devicefurther includes a pair of arm motor assemblies(individually identified as a first arm motor assemblyand a second arm motor assembly) coupled to the upper supportand operably coupled to the arm assembly.is an isometric view of the arm assemblyand arm motor assemblies, configured in accordance with representative embodiments of the present technology. Referring totogether, more specifically, the second shaftcan include a first end portionoperably coupled to the first arm motor assemblyand a second end portionoperably coupled to the second arm motor assembly. The arm motor assembliescan include a motor (e.g., a rotary motor) and associated gearbox and are configured to drive the second shaft() to rotate about the second axis Ato drive the arm assemblyto pivot about the second axis Ain a first direction and/or a second direction as indicated by arrows Fand F, respectively, in. In some embodiments, the arm assemblyis constrained (e.g., via one or more mechanical means) to pivot about the second axis Ain the direction of arrows Fand Fby a selected (e.g., predetermined) maximum amplitude. In some embodiments, the arm motor assembliesare identical and are positioned and oriented to be symmetric about the first axis A. Accordingly, the arm motor assembliescan together define a center of mass positioned along or substantially along the first axis A. In some embodiments, the devicecan include only a single one of the arm motor assembliesor more than two of the arm motor assemblies.

3 FIG. 1 1 FIGS.A-C 1 FIG.A 110 112 110 334 334 334 112 126 334 114 114 114 334 334 100 334 334 a b a b a b 3 1 2 3 1 2 1 2 2 is an isometric side view of the arm assemblywith the housing() omitted for clarity in accordance with embodiments of the present technology. In the illustrated embodiment, the arm assemblyincludes a pair of rotor motor assemblies(individually identified as a first rotor motor assemblyand a second rotor motor assembly) secured within the housingon opposing sides of the second shaft. The first and second rotor motor assemblies-can each include a motor (e.g., a rotary motor) and associated gearbox and are configured to drive the first rotorand the second rotor, respectively, to pivot about the third axis Ain a first direction and/or a second direction as indicated by arrows Gand G, respectively, in. In some embodiments, the rotorsare constrained (e.g., via one or more mechanical means) to pivot about the third axis Ain the direction of arrows Gand Gby a selected (e.g., predetermined) amplitude. In some embodiments, the rotor motor assembliesare identical and are positioned and oriented to be symmetric about the first axis Aand the second axis A. Accordingly, the rotor motor assembliescan together define a center of mass positioned along or substantially along the second axis A. In some embodiments, the devicecan include only a single one of the rotor motor assembliesor more than two of the rotor motor assemblies.

3 FIG. 114 114 114 335 334 336 337 335 335 336 336 335 114 114 114 114 114 126 114 110 100 114 110 3 3 3 2 With continued reference to, in some embodiments the rotorscan be identical—for example, having the same shape, mass, density, geometry, and/or the like. In some embodiments, the rotorscan have a wheel-and-spoke shape such that they are each symmetric about the third axis A. More specifically, the rotorscan each include a central portioncoupled to the corresponding one of the rotor motor assemblies, an outer portion(e.g., an outer ring), and a plurality of spokesextending radially outward from the central portionand the third axis Aand connecting the central portionto the outer portion. In some embodiments, the outer portioncan have a greater mass than the central portionsuch that a majority of the mass of the rotoris positioned radially outward from the third axis A. In some embodiments, the rotorscan have different shapes, sizes, and/or configurations, and/or one of the rotorscan be omitted. For example, in some embodiments each of the rotorscan have a planar disc-shape. In some embodiments, the rotorsare each positioned at a distance D from the second shaftand the second axis Aand each have a radius R. The distance D, the radius R, and/or the shape of the rotorscan be selected to change the inertia and/or torque-summing properties of the arm assemblyas described in greater detail below. In some embodiments, the deviceincludes only one of the rotorssuch that the arm assemblyis pendulously arranged.

1 1 FIGS.A andB 3 FIG. 100 140 142 144 146 148 140 130 132 334 122 100 130 132 334 141 140 Referring totogether, the devicecan further include a control and power subsystemthat in turn includes one or more power sources, one or more sensors, one or more power generators, and a controller. The control and power subsystemcan be operably coupled to the shaft motor assembly, the arm motor assemblies, the rotor motor assemblies(), the brake mechanism, and/or other components of the devicevia wired and/or wireless connections. For example, in the illustrated embodiment the shaft motor assembly, the arm motor assemblies, and the rotor motor assemblieseach have one or more electrical connectorsthat can be electrically coupled to the control and power subsystemfor passing data, power, and/or other signals therebetween.

142 143 108 142 130 132 334 144 120 110 114 130 132 334 100 146 146 120 120 1 FIG.B The power sourcecan be an AC power source and/or a DC power source and, in some embodiments, can include/comprise a servo drive() coupled to the upper supportor elsewhere. The power sourcecan provide electrical power to the shaft motor assembly, the arm motor assemblies, and the rotor motor assemblies. The sensorscan include one or more sensors configured (e.g., positioned) for detecting (i) a rotational and/or pivotal rate of the first shaft, the arm assembly, and/or the rotors, (ii) a power usage of the shaft motor assembly, the arm motor assemblies, and/or the rotor motor assemblies, and/or (iii) a power output of the device(e.g., via the power generator), and/or the like. The power generatorcan be or can include a dynamo or other suitable generator coupled to the first shaftfor converting the mechanical rotation of the first shaftto electrical energy.

146 130 130 120 120 146 120 146 142 130 132 334 146 142 142 146 132 132 126 126 In some embodiments, the power generatorcan comprise/include the shaft motor assembly. That is, the shaft motor assemblycan drive the first shaftto rotate in a first operating configuration and convert the rotation of the first shaftto electrical energy in a second operating configuration. In some embodiments, the power generatorcan be or can include a mechanical device for converting the mechanical rotation of the first shaftto another useful output. In some embodiments, the power generatorcan generate electrical energy and provide the electrical energy to the power sourceor directly to the shaft motor assembly, the arm motor assemblies, and/or the rotor motor assemblies. That is, the power generatorcan function as the power sourceand/or can provide feedback to the power source. In other embodiments, the power generatorcan comprise/include one or both of the arm motor assemblies. That is, the arm motor assembliescan drive the second shaftto pivot in a first operating configuration and convert the pivotable motion of the second shaftto electrical energy (and/or another useful output, such as mechanical energy) in a second operating configuration.

148 144 142 130 132 334 148 130 120 132 110 334 114 148 149 108 1 2 3 1 FIG.B The controllercan receive data from the sensorsand control the power sourceto operate the shaft motor assembly, the arm motor assemblies, and/or the rotor motor assemblies. Specifically, as described in further detail below, the controllercan cause (i) the shaft motor assemblyto rotate the first shaftat a selected (e.g., predetermined) rotational rate about the first axis A, (ii) the arm motor assembliesto pivot the arm assemblyabout the second axis Aat a selected amplitude and frequency, and (iii) the rotor motor assembliesto pivot the rotorsabout the third axis Aat a selected amplitude and frequency. In some embodiments, the controllercan include/comprise a printed circuit board (PCB)() coupled to the upper supportor elsewhere.

148 148 The controllercan comprise a processor and a non-transitory computer-readable storage medium that stores instructions that, when executed by the processor, carry out the functions attributed to the controlleras described herein. Although not required, aspects and embodiments of the present technology can be described in the general context of computer-executable instructions, such as routines executed by a general-purpose computer (e.g., a server or personal computer). Those skilled in the relevant art will appreciate that the present technology can be practiced with other computer system configurations, including Internet appliances, hand-held devices, wearable computers, cellular or mobile phones, multi-processor systems, microprocessor-based or programmable consumer electronics, set-top boxes, network PCs, mini-computers, mainframe computers and the like. The present technology can be embodied in a special purpose computer or data processor that is specifically programmed, configured and/or constructed to perform one or more of the computer-executable instructions explained in detail below. Indeed, the terms “controller” and “computer” (and like terms), as used generally herein, refers to any of the above devices, as well as any suitable data processor or any suitable device capable of communicating with a network, including consumer electronic goods or other electronic devices having a processor and other components (e.g., network communication circuitry).

The present technology can also be practiced in distributed computing environments, where tasks or modules are performed by remote processing devices, which are linked through a communications network, such as a Local Area Network (“LAN”), Wide Area Network (“WAN”), or the Internet. In a distributed computing environment, program modules or sub-routines can be located in both local and remote memory storage devices. Aspects of the present technology described below can be stored or distributed on computer-readable media, including magnetic and optically readable and removable computer discs, stored as in chips (e.g., EEPROM or flash memory chips). Alternatively, aspects of the present technology can be distributed electronically over the Internet or over other networks (including wireless networks). Those skilled in the relevant art will recognize that portions of the present technology can reside on a server computer, while corresponding portions reside on a client computer. Data structures and transmission of data particular to aspects of the present technology are also encompassed within the scope of the present technology.

140 130 132 334 120 110 114 100 120 110 114 130 120 110 110 110 110 132 110 110 110 110 110 1 3 FIGS.A- 1 FIG.A 1 2 3 1 2 1 2 2 In some embodiments, the control and power subsystem, the shaft motor assembly, the arm motor assemblies, the rotor motor assembliescan together be referred to as a “control system” or the like for controlling the motion of the first shaft, the arm assembly, and the rotors. Referring totogether, in general during operation of the device, the control system is configured to control a rotation rate of the first shaftabout the first axis A, a frequency and/or amplitude of oscillation of the arm assemblyabout the second axis A, and a frequency and/or amplitude of oscillation of the rotorsabout the third axis A. More specifically, the shaft motor assemblycan direct the first shaftand the coupled arm assemblyto rotate about the first axis Aat and/or to a selected rotational rate. The rotating arm assemblygenerates a centrifugal force that acts against the arm assemblyto oscillate the arm assemblyabout the second axis Ain the directions indicated by arrows Fand Fin. In some embodiments, the arm motor assembliescan drive the arm assemblyabout the second axis A(augmenting the centrifugal force acting against the arm assembly) such that the arm assemblyoscillates at a selected frequency and maximum amplitude. The resulting motion of the arm assemblycan be periodic (e.g., sinusoidal). The maximum angular amplitude is limited by the torque due to the centrifugal force from the rotation of the arm assembly.

334 114 114 114 114 114 114 3 1 2 3 1 FIG.A a b The rotor motor assembliescan drive the rotorsto pivot about the third axis Ain an oscillatory/modulated manner in which the rotorspivot in the directions indicated by arrows Gand G() about the third axis Ato a selected frequency and maximum angular amplitude. The resulting motion of the rotorscan be periodic (e.g., sinusoidal). In some embodiments, the periodic motion of the first rotoris opposite (e.g., 180 degrees out of phase with) the periodic motion of the second rotorand at the same frequency such that the rotorsmove in opposite directions past one another and reach their maximum angular amplitudes in opposite directions at the same time or at least approximately the same time.

142 132 334 110 114 114 110 120 120 120 110 110 114 120 120 146 1 2 In some embodiments, the power sourcecan supply an oscillatory/modulated voltage to the arm motor assembliesand the rotor motor assembliesto generate the oscillatory motion of the arm assemblyand the rotors. The oscillatory angular momentum of the rotorsand the arm assemblytogether exert a gyroscopic torque on the first shaftabout the first axis Athat acts to rotate the first shaft. Accordingly, the rotation of the first shaftdrives the arm assemblyto oscillate about the second axis A, and the resulting oscillation of the arm assemblyand the oscillation of the rotorsacts to drive the rotation of the first shaftin a feed-back loop. The mechanical rotation of the first shaftcan be coupled to the power generatorfor generating output power.

4 FIG. 1 3 FIGS.A- 100 334 450 114 114 451 110 452 451 452 454 453 454 120 455 120 459 146 120 110 456 110 110 452 110 456 456 110 452 110 3 2 1 2 2 2 is block diagram more specifically illustrating representative physical properties/forces as the deviceoperates in accordance with embodiments of the present technology. With additional reference to, in the illustrated embodiment, the rotor motor assembliesprovide a drive forcethat oscillates the rotorsabout the third axis A. The oscillation of the rotorsgenerates an oscillatory rotor angular momentum. The oscillation of the arm assemblyabout the second axis Agenerates an oscillatory arm assembly angular velocity. The oscillatory rotor angular momentumand the oscillatory arm assembly angular velocitygenerate a gyroscopic torqueabout the first axis Adefined as the vector cross-productthereof. The gyroscopic torquehas an oscillating magnitude and average value, which drives the first shaftto rotate at a rotational rate. The rotation of the first shaftcan deliver mechanical energy to an output load, such as the power generator. The rotation of the first shaftalso rotates the arm assembly, thereby generating a centrifugal forceon the arm assemblythat acts to oscillate the arm assemblyabout the second axis Aand generate the oscillatory arm assembly angular velocity. Torque generated on the arm assemblyby the centrifugal forcereaches a maximum value when the arm assembly is oriented at a 45 degree angle relative to the second axis A(e.g., above or below horizontal) and is always directed toward the horizontal. As such, the torque due to the centrifugal forcecan (i) be the primary force that drives the arm assemblyto have the oscillatory arm angular velocityand (ii) limit the angular excursion of the arm assemblyabout the second axis A(e.g., with a maximum angular excursion typically of about 45 degrees).

130 457 454 455 120 130 457 100 120 132 458 110 452 In some embodiments, the shaft motor assemblycan provide an auxiliary drive forcethat augments the gyroscopic torqueto control the rotational rateof the first shaft. In some embodiments, the shaft motor assemblycan provide the input auxiliary drive forceinitially during startup of the deviceuntil the first shaftis rotating at or near a desired rotational rate. Likewise, in some embodiments the arm motor assembliescan provide an auxiliary drive forcethat oscillates the arm assemblyto control the oscillatory arm assembly angular velocity.

100 454 120 110 110 114 120 110 114 120 110 114 120 110 114 110 114 120 454 100 120 110 110 114 1 2 3 1 2 3 In some embodiments, the deviceis configured to operate in a “resonant” mode or at least approximately resonant mode (e.g., within at least 1%, 2%, 5%, 8%, or 10% of resonance) in which the gyroscopic torqueis maximized or approximately maximized. In some embodiments, in the resonant mode, the rotational rate of the first shaft(and the arm assembly) about the first axis Aequals or at least approximately equals an oscillation frequency of the arm assemblyabout the second axis Aand an oscillation of frequency of the rotorsabout the third axis A. For example, if the first shaftrotates at 18 rotations per second, the arm assemblyand the rotorscan each have an oscillation frequency of 18 hertz in the resonant mode. In some embodiments, in the resonant mode, the rotational rate of the first shaftis different (e.g., slightly different) than the oscillation frequency of the arm assemblyand/or the oscillation frequency of the rotors. That is, there can be a slight dissonance in the rotational rate of the first shaft, the oscillation frequency of the arm assembly, and/or the oscillation frequency of the rotors. For example, if the arm assemblyand the rotorseach have an oscillation frequency of 18 hertz, the first shaftcan rotate at between about 15-21 rotations per second, and at a rotation rate different than 18 rotations per second, in the resonant mode in which the gyroscopic torqueis maximized or approximately maximized. In other embodiments, the devicecan operate in a “non-resonant” mode of operation in which the rotational rate of the first shaft(and the arm assembly) about the first axis Adoes not equal the oscillation frequency of the arm assemblyabout the second axis Aand the oscillation of frequency of the rotorsabout the third axis A.

100 110 114 114 110 451 452 451 452 451 452 114 110 451 452 451 452 451 452 5 5 FIGS.A andB 4 FIG. 1 5 FIGS.A-B 5 5 FIGS.A andB 5 FIG.A 5 FIG.B max max Additionally, the devicecan drive the arm assemblyand/or the rotorsto adjust a phase angle and/or phase relationship between the oscillations of the rotorsand the arm assembly—and thus a phase angle between the associated oscillatory rotor angular momentumand the associated oscillatory arm assembly angular velocity.are graphs illustrating components of the oscillatory rotor angular momentumand the oscillatory arm assembly angular velocityofover time in accordance with embodiments of the present technology. Referring totogether, the oscillatory rotor angular momentumand the oscillatory arm assembly angular velocitycan each be periodic due to the oscillatory motion of the rotorsand the arm assembly, respectively. The oscillatory rotor angular momentumcan have a maximum amplitude Mand the oscillatory arm assembly angular velocitycan have a maximum amplitude V. Inthe oscillatory rotor angular momentumand the oscillatory arm assembly angular velocityhave the same frequency (e.g., as in the resonant mode of operation). The oscillatory rotor angular momentumand the oscillatory arm assembly angular velocityare offset by a phase angle Φ inand are in phase (e.g., Φ=0) in.

100 451 452 114 110 100 454 120 148 132 334 110 114 451 452 453 454 454 451 452 In some embodiments, the deviceis configured to adjust the phase angle Φ (and/or another phase relationship) between the oscillatory rotor angular momentumand the oscillatory arm assembly angular velocity(and the corresponding motion of the rotorsand the arm assembly) to an optimum value such that the deviceoperates in the resonant or substantially resonant mode and/or maximizes the gyroscopic torqueapplied to the first shaft. To effect such a change in the phase angle Φ, the controllercan control the arm motor assembliesand/or the rotor motor assembliesto adjust the oscillations of the arm assemblyand/or the rotors, respectively. Because the oscillatory rotor angular momentumand the oscillatory arm assembly angular velocityare each sinusoidal (or quasi-sinusoidal), the vector cross-productbetween them will yield an average value of the gyroscopic torqueand a second harmonic. The average value of the gyroscopic torqueis dependent on the phase angle Φ, and is zero when the oscillatory rotor angular momentumand the oscillatory arm assembly angular velocityare in quadrature.

454 454 100 100 110 114 110 114 110 In some embodiments, the average value of the gyroscopic torqueis maximized when the phase angle Φ is 0 degrees or 180 degrees. However, the optimum phase angle Φ that maximizes the value of the gyroscopic torquecan have values other than 0 degrees or 180 degrees based on the operating conditions of the device. In particular, the devicemay generate other torques on the arm assemblyand/or the rotorsthat inhibit or even prevent the oscillations of the arm assemblyand the rotorsfrom being totally in phase—that is, such that the arm assemblyand the rotors have an oscillation component that is always out of phase.

6 FIG. 1 5 FIGS.A-B 650 650 100 650 is a flow diagram of a method or processfor operating representative devices to generate power in accordance with embodiments of the present technology. Although some features of the methodare described in the context of the devicedescribed in detail with reference tofor the sake of illustration, one skilled in the art will readily understand that the methodcan be carried out using other suitable devices and/or systems described herein.

651 650 120 110 130 120 110 454 130 120 454 130 454 1 Beginning at block, the methodincludes rotating the first shaft(e.g., a drive shaft) and the arm assemblyattached thereto about the first axis Aat a selected rotational rate. In some embodiments, the shaft motor assemblycan provide an initial (start-up) torque to rotate the first shaftuntil the arm assemblygenerates the gyroscopic torque, at which point the torque from the shaft motor assemblycan be reduced or eliminated and the rotation of the first shaftdriven entirely or substantially entirely by the generated gyroscopic torque. In some embodiments, the shaft motor assemblycan be omitted and instead rotated entirely by the generated gyroscopic torque.

652 650 110 132 110 456 110 132 110 456 132 110 452 451 2 At block, the methodincludes pivoting the arm assemblyin an oscillatory manner about the second axis Aat a first frequency. In some embodiments, the arm motor assembliescan provide an initial (start-up) torque to rotate the arm assemblyuntil the centrifugal forceacts to oscillate the arm assembly—at which point the torque from the arm motor assembliescan be reduced or eliminated and the oscillation of the arm assemblydriven entirely or substantially entirely by the generated centrifugal force. In some embodiments, the arm motor assembliescan be used only to adjust the frequency of the oscillation of the arm assembly(and a resulting phase relationship between the generated oscillatory arm assembly angular velocityand the oscillatory rotor angular momentum.

653 650 114 120 651 110 652 114 653 100 452 100 451 114 454 120 120 110 456 110 3 At block, the methodincludes pivoting the rotorsin an oscillatory manner about the third axis Aat a second frequency. As described in detail above, when the first shaftis rotating (block), the arm assemblyis oscillating (block), and (the rotorsare oscillating (block), the deviceincludes a feedback loop in which (i) the angular velocityof the arm assemblyand the angular momentumof the rotorscombine to generate a gyroscopic torquethat acts to rotate the first shaft, and (ii) the rotation of the first shaftrotates the arm assemblyto generate a centrifugal forcethat acts to oscillate the arm assembly.

654 650 459 120 459 100 120 100 At block, the methodincludes applying the output loadto the first shaft. The output loadextracts energy from the device—acting to slow the rotational rate of the first shaftabsent any adjustments to the operating parameters of the device.

655 650 100 120 110 114 100 454 120 459 100 100 459 110 114 148 100 459 100 100 120 110 114 100 120 110 114 At block, the methodincludes controlling the deviceto operate in the resonant mode in which the rotational rate of the first shaftequals or is at least approximately equal to both the first frequency of oscillation of the arm assemblyand the second frequency of oscillation of the rotors. In some embodiments, controlling the deviceto operate in the resonant mode includes setting/adjusting the phase angle Φ to increase the gyroscopic torqueapplied to the first shaftto compensate for the loadand maintain the resonant mode of operation. Accordingly, in some aspects of the present technology the phase angle Φ can control the resonance of the device. In some embodiments, the devicecan be specifically designed for a known load such that the phase angle Φ need not be adjusted/set during operation. However, in some embodiments the loadcan be variable and the oscillations of the arm assemblyand/or rotorscan be controlled automatically by the controlleror manually by a user to maintain the devicein the resonant mode during variations in the load. In other embodiments, controlling the deviceto operate in the resonant mode includes controlling the devicesuch that the rotational rate of the first shaftis different (e.g., slightly different) than the first frequency of oscillation of the arm assemblyand/or the second frequency of oscillation of the rotors. That is, the devicecan be operated with a slight dissonance in the rotational rate of the first shaft, the first frequency of oscillation of the arm assembly, and/or the second frequency of oscillation of the rotorsto promote/create a centrifugal resonance in which gyroscopic torques are maximized.

100 120 459 100 130 132 334 454 334 114 132 110 100 In some aspects of the present technology, it is expected that the net energy output from the device(e.g., via the first shaftto the load) will exceed the net energy input into the devicevia, for example, the shaft motor assembly, the arm motor assemblies, and/or the rotor motor assemblies. That is, for example, the net mechanical power available from the gyroscopic torquecan exceed the sum of the input power to the rotor motor assembliesthat drives the rotorsand the input power to the arm motor assembliesthat provides auxiliary power to the arm assemblyfor controlling the phase angle Φ—even when considering impediments (e.g., friction and/or other losses) to the various components of the device.

100 120 110 100 120 110 114 100 1 2 3 Section II below, for example, models the motion of the devicewith equations. In Section II, the first axis Ais referred to as a “spindle axis,” the second axis Ais referred to as a “hinge axis,” the third axis Ais referred to as a “rotor axis,” the first shaftis referred to as a “spindle,” and the arm assemblyis referred to as an “arm.” As outlined in Section II, the difference between the output power and the total input power of the deviceis dependent on the phase angle Φ and, even factoring in impediments to the motion of the first shaft, the arm assembly, and/or the rotors, there can be a range of phase angles for which the output is greater than the input. For example, as shown in Section II, the devicecan generate net power (e.g., output power greater than input power) for phase angles Φ between about 5-75 degrees and can generate a maximum amount of net power when the phase angle Φ is between about 30-45 degrees (e.g., about 40 degrees).

100 120 100 100 130 132 334 100 120 100 In some aspects of the present technology, the devicecan provide an energy output via the first shaftthat is more efficient than conventional motor assemblies—even if the power output from the deviceis not greater than the power input to the device. Specifically, the power inputs to the shaft motor assembly, the arm motor assemblies, and/or the rotor motor assembliescan each be relatively small compared to the total power output of the device. Such smaller motors can be relatively more efficient than a comparable motor assembly configured to directly rotate the first shaftat the same output power. Therefore, the arrangement of the deviceadvantageously allows for the power inputs from several smaller motor assemblies to drive a series of motions (e.g., oscillations and rotations) that efficiently combine to generate a relatively great power output.

100 100 100 114 114 110 110 110 114 110 120 In general, the operating/design parameters of the devicecan be optimized to maximize power output (e.g., based on the equations detailed in Section II) based on a selected application of the device. For example, the devicecan have a small form factor (e.g., for powering a watch or cell phone), a medium form factor (e.g., for powering home appliances), a large form factor (e.g., for powering a remote well or lift station), and so on. Depending on the application, the operating/design parameters that can be optimized include: (i) the oscillation frequency of the rotors, (ii) the oscillation amplitude of the rotors, (iii) the oscillation frequency of the arm assembly, (iv) the oscillation amplitude of the arm assembly, (v) the number of arm assemblies(e.g., including one or more arm assemblies), (vi) the number of rotorsmounted to each of the arm assemblies, (vii) the rotation rate of the first shaft, (viii) the size and/or mass of any of the components which can directly affect the inertia, momentum, velocity, and/or forces generated by the components, among others. For example, Sections III and IV below provide examples of representative design parameters that can be selected for a centrifugal gyroscopic device in accordance with the present technology that-even when considering impediments—can operate very efficiently or even to produce more output than input.

7 FIG. 1 6 FIGS.A- 7 FIG. 700 700 700 100 100 700 720 710 720 714 714 714 740 710 714 720 1 2 3 2 3 1 a b is a perspective side view of a centrifugal gyroscopic device(“device”) configured in accordance with additional embodiments of the present technology. The devicecan include some features that are at least generally similar in structure and function, or identical in structure and function, to the corresponding features of the devicedescribed in detail above with reference to, and can operate in a generally similar or identical manner to the device. In the illustrated embodiment, for example, the deviceincludes: (i) a drive shaftrotatable along the first axis A, (ii) an arm assemblyrotatable with the drive shaftand pivotable about the second axis A, (iii) a pair of rotors(identified individually as a first rotorand a second rotor) pivotable about the third axis A, and (iv) a control and power subsystemoperable to drive (via one or more motor assemblies) the arm assemblyto oscillate about the second axis A(extending into the page in) and the rotorsto oscillate about the third axis A(and/or to drive the drive shaftto rotate about the first axis A).

700 720 710 710 714 700 710 714 710 720 720 720 720 1 2 3 1 1 8 8 FIGS.A-D 8 8 FIGS.A-D 8 8 FIGS.B andD In some embodiments, the deviceis configured to operate in a resonant mode or substantially resonant mode in which the rotational rate of the drive shaft(and the arm assembly) about the first axis Aequals or substantially equals an oscillation frequency of the arm assemblyabout the second axis Aand an oscillation of frequency of the rotorsabout the third axis A.are enlarged perspective views of the deviceillustrating the movement of the arm assemblyand the rotorsduring one complete revolution of the arm assemblyabout the first axis Ain the resonant mode of operation in accordance with embodiments of the present technology.sequentially illustrate the arm assemblyat different quarter (e.g., 90 degrees) revolutions about the first axis A. If the rotation of the arm assemblyis at a sufficient rate to blur the oscillatory movement of the arm assembly, an optical illusion presents itself that the axis of rotation of the arm assemblyis tilted by the angle shown in.

8 FIG.A 8 FIG.A 710 710 714 3 1 1 3 3 In, the arm assemblyextends generally parallel to the horizontal (e.g., horizontal to gravity). That is, the third axis Aextends orthogonal to the first axis A(e.g., such that an angle between the first and third axes A, Ais about 90 degrees). Accordingly, the arm assemblycan have a minimum angular amplitude in the position in shown. Further, the rotorsare each at a first angular position relative to the third axis A.

8 FIG.B 8 FIG.A 8 FIG.B 8 FIG.B 8 FIG.A 710 710 714 714 720 714 710 714 714 720 b a 3 In, the arm assemblyhas rotated by about 90 degrees (e.g., in a clockwise direction) about the first axis Aj from the position shown inand such that arm assemblyextends at angle T relative to the horizontal. In the illustrated embodiment, the second rotoris positioned above the first rotorrelative to the horizontal. In some embodiments, the angle T can be a maximum angular amplitude of the oscillation of the arm assembly. Further, the rotorsare each at a second angular position relative to the third axis Ain. In some embodiments, where the phase of the arm assemblyand the rotorsis generally the same (e.g., phase angle equal to zero), the rotorscan—the same as the arm assembly—have a maximum angular amplitude inand a minimum angular amplitude in.

8 FIG.C 8 FIG.B 8 FIG.C 710 710 714 710 714 1 3 In, the arm assemblyhas rotated by about 90 degrees (e.g., in a clockwise direction) about the first axis Afrom the position shown inand such that the arm assemblyextends generally parallel to the horizontal and again has the minimum angular amplitude. The rotorsare each at a third angular position relative to the third axis Ain. In the resonant mode where the oscillation frequency of the arm assemblyequals the oscillation frequency of the rotors, the third angular position can be the same as the first angular position (e.g., both at the minimum angular amplitude) or the third angular position can have the opposite sign as the first angular position.

8 FIG.D 8 FIG.C 8 FIG.D 710 710 714 714 714 710 714 1 3 a b In, the arm assemblyhas rotated by about 90 degrees (e.g., in a clockwise direction) about the first axis Afrom the position shown inand such that arm assemblyextends again at the angle T relative to the horizontal. In the illustrated embodiment, however, the first rotoris positioned above the second rotorrelative to the horizontal. The rotorsare each at a fourth angular position relative to the third axis Ain. In the resonant mode where the oscillation frequency of the arm assemblyequals the oscillation frequency of the rotors, the fourth angular position can be the same as the second angular position (e.g., both at a maximum angular amplitude) or the fourth angular position can have the opposite sign as the second angular position.

710 700 710 714 714 100 8 FIG.A 8 8 FIGS.A-D 8 8 FIGS.A-D 7 FIG. 8 8 FIGS.B andD 8 8 FIGS.B andD 2 1 1 The arm assemblycompletes a revolution by returning to the position shown in. Referring totogether, the movement of the devicein the resonant mode can create an optical illusion when viewed from the side at a particular azimuthal angle as shown in. Namely, the arm assemblycan appear to be consistently pivoted about the second axis A() off vertical (e.g., typically at a tilt angle of 45 degrees) in a particular direction. This occurs because, for example, the rotorseach reach a maximum angular amplitude below horizontal when located at the same or approximately the same circumferential position about the first axis A(e.g., to the left of the page as shown in). Similarly, the rotorseach reach a maximum angular amplitude above horizontal when located at the same or substantially the same circumferential position about the first axis A(e.g., to the right of the page as shown in). In some embodiments, the optical illusion will rotate in azimuth when the deviceis off resonance.

9 FIG. 10 FIG. 11 FIG. 120 120 120 is a schematic diagram of a control assembly for controlling a spindle (e.g., the first shaft) in accordance with embodiments of the present technology.is a schematic diagram of a control assembly for controlling a spindle (e.g., the first shaft) in accordance with additional embodiments of the present technology.is a schematic diagram of an analog control assembly for controlling a spindle (e.g., the first shaft) in accordance with additional embodiments of the present technology.

A set of gyroscopic axes is defined by the vector cross-product, according to the righthand rule. The axes are termed the rotor reference axis, the spindle axis, and the hinge axis. For convenience, the spindle axis is considered to be vertical. If the rotor axis is at an angle to the rotor reference axis about the hinge axis, the vector cross-product automatically takes it into account. The vector cross-product of (vector along the rotor axis)×(vector along the spindle axis) yields a (vector along the hinge axis). Similarly, the vector cross-product of (vector along the spindle axis)×(vector along the hinge axis) yields a (vector along the rotor axis). And, similarly, the vector cross-product of (vector along the hinge axis)×(vector along the rotor axis) yields a (vector along the spindle axis). Reverse vector cross-products are also applicable. Specifically, the vector cross-product of (vector along the spindle axis)×(vector along the rotor axis) yields a (vector along the negative hinge axis). Similarly, the vector cross-product of (vector along the hinge axis)×(vector along the spindle axis) yields a (vector along the negative rotor axis). And, similarly, the vector cross-product of (vector along the rotor axis)×(vector along the hinge axis) yields a (vector along the negative spindle axis). The six vector cross-products are summarized as follows:

R S τ=unit vector along spindle axis H τ=unit vector along hinge axis where: τ=unit vector along rotor axis

In terms of gyroscopic action, each vector can represent either angular momentum or angular velocity. The vector cross-product of angular momentum and its angular velocity about an orthogonal axis yields a gyroscopic torque about the third axis. Thus, in general, the angular momentum of the rotor, arm, and spindle can each have an angular velocity about either of the two orthogonal axes, yielding six combinations of gyroscopic torque.

In this particular case, the spindle has only one degree of freedom, that is, rotation about the spindle axis. Therefore, its angular momentum is restricted from rotating about an orthogonal axis, thus eliminating two of the generalized gyroscopic torques, leaving four.

Also, the arm is prohibited from rotating about the rotor axis. Therefore, the gyroscopic torque that would arise from the angular momentum of the arm being rotated about the rotor axis is eliminated, leaving three. Further, although the spindle rotates the angular momentum of the arm, thus exerting a gyroscopic torque on the arm about the rotor axis, the arm is prohibited from rotating about the rotor axis. This gyroscopic torque exerts a stress on the supporting structure of the hinge axis. With the elimination of this gyroscopic torque as having an effect on the dynamic motion in the system, there remain two gyroscopic torques that do affect the dynamic motion of the system. The two gyroscopic torques that are effective are as follows:

R/R R/R ω=angular velocity of rotor about rotor axis R/S ω=angular velocity of rotor and arm about spindle axis R/H ω=angular velocity of rotor and arm about hinge axis A/H θ=arm angle off horizontal about hinge axis R/S M=gyroscopic torque on rotor and arm about spindle axis R/H M=gyroscopic torque on rotor and arm about hinge axis where: I=moment of inertia of rotor about rotor axis

If the angular momentum about one axis and its velocity about an orthogonal axis are both constant, the gyroscopic torque about the third axis is constant. If either the angular momentum or angular velocity is oscillatory and the other is constant, the gyroscopic torque is oscillatory. If both the angular momentum and angular velocity are oscillatory at the same frequency, the gyroscopic torque has two components, a constant (which is zero, if the oscillations are in quadrature, that is, 90 degrees apart in phase) and a second harmonic.

For an arm that is balanced along the rotor reference axis and along the spindle axis, the differential equations for rotor oscillation about the rotor axis, spindle rotation, and arm oscillation about the hinge axis, respectively, are given by:

R S/S I=Moment of inertia of spindle (including arm) about spindle axis A/H I=Moment of inertia of arm about hinge axis R/R {umlaut over (θ)}=Angular acceleration of rotor about rotor axis S {umlaut over (θ)}=Angular acceleration of spindle about spindle axis A/H {umlaut over (θ)}=Angular acceleration of arm about hinge axis R/R {dot over (θ)}=Angular velocity of rotor about rotor axis S {dot over (θ)}=Angular velocity of spindle about spindle axis A/H {dot over (θ)}=Angular velocity of arm about hinge axis A/H θ=Angle of arm horizontal R IN (M)=Input torque for rotor oscillation S IN (M)=Input torque for startup of spindle rotation A M (M)=Input torque about hinge axis R I (M)=Impediment torque to rotor oscillation about rotor axis A I (M)=Impediment torque to arm oscillation about hinge axis S I (M)=Impediment torque to spindle rotation LOAD M=Load torque on spindle A m=Mass of arm G/R r=Radius of gyration along rotor reference axis G/S r=Radius of gyration along spindle axis where: I=Moment of inertia of rotor about rotor axis

The equations are mathematically intractable, mainly because the expression for the torque due to centrifugal force contains the product of the sine and cosine of the angle of the arm about the hinge axis, which itself is a quasi-sinusoidal function. A closed form solution is available under ideal impediment-free conditions and small amplitudes of oscillation where small-angle approximations are valid.

The spindle velocity is assumed to be constant. The phase of the torque from the motor is assumed to be in phase with the rotor angular acceleration. The rotor and arm are oscillated with the same frequency of oscillation. The differential equation for motion about the hinge/arm axis can be rewritten with slightly different nomenclature, as follows:

A I=Moment of inertia of arm and rotor about the arm axis R I=Moment of inertia of rotor about rotor axis A M=Torque provided by arm motor S ω=Angular velocity of spindle C I=Constant relating spindle speed to centrifugal torque on arm

A,max The arm position is assumed to have the amplitude θat time t=0. The rotor acceleration and the arm torque have a phase φ relative to the arm position.

R A let ω=ω=ω=frequency of oscillation S let ω=ω A R Mand {umlaut over (θ)}are in phase R R,max {dot over (θ)}=−ωθcos (ωt+φ) R R,max 2 {umlaut over (θ)}=−ωθsin (ωt+φ) R R,max 2 {umlaut over (θ)}=−ωθcos (ωt+φ)

Substitute these values for rotor and arm positions, velocities, and accelerations into the torque equation.

Replace cos (ωt) with

Collecting the sin (ωt+φ) terms results in:

Define

Resonance for the arm would occur at

o S C A which implies that ω<ωsince I<I.

S There is no resonance for the arm for ω=ω. True, resonance is indicated when spindle speed is a bit higher than the oscillating frequency of the rotors and arm, if the small-angle approximations were still valid at large amplitudes and with impediment torques acting on the arm. The stiffness afforded by the centrifugal-forced torque is not constant at larger amplitudes. Nevertheless, it is an intriguing notion as to whether some resonant-like behavior can be used to advantage at larger amplitudes. As a cautionary note, as arm amplitudes of oscillation are enlarged, they become subject to limitations imposed by centrifugal effects.

There is no indication of resonance for the rotor.

Collecting the cos (ωt+φ) terms gives:

Dividing these two equations:

The gyroscopic torque applied to the spindle is given by this equation:

Integrate with respect to time to get the average gyroscopic torque. The sin (2ωt) and the sin (ωt) terms integrate to zero.

A,max As was mentioned for θpreviously, if the solution with small-angle approximations is a harbinger of performance in general, the average gyroscopic torque can be enlarged by approaching resonance.

R,max Replace θwith expression above from sin terms:

When the spindle is used as the source of output power, it is not convenient to compare the output torque with the input torques, because the output is an average value and the input torques are oscillatory. However, the output power can be compared to the total input power. The output power is the product of the average output torque and the spindle rate. Each input power is the average power over a quarter oscillatory cycle (being independent of algebraic signs and being the same in each of the other three quarters) and is given by the average of the product of the oscillatory input torque and the instantaneous angular velocity attributed to input torque. The expressions for output power and input power to the rotor and to the arm by an auxiliary motor are given by:

The difference between the output power and total input power can be expressed in normalized fashion as follows:

12 FIG. is a graph illustrating normalized net power versus the phase angle between rotor and arm oscillations. As shown, the normalized net power depends on the phase angle between the rotor and arm oscillations for a practical set of design geometries. There is a range of phase angles where the output is greater than the input.

Alternately, the input power is given by the in-phase component of the product of torque and velocity. The expressions for the rotor and arm motors are:

P-in-a=input power from arm motor (watts) M-r-max=amplitude of torque provided by rotor motor (N-m) M-a-max=amplitude of torque provided by arm motor (N-m) Kt-r=torque constant for rotor motor (N-m/amp) Kt-a=torque constant for arm motor (N-m/amp) Amp-r-max=amplitude of current in rotor motor (amp) Amp-a-max=amplitude of current in arm motor (amp) w-r-max=amplitude of rotor angular velocity about rotor axis (rad/sec) w-a-max=amplitude of arm angular velocity about arm axis (rad/sec) f=frequency of oscillation of rotor and arm (hz) phi-r=phase angle between rotor torque and angular velocity waveforms (rad) phi-a=phase angle between arm torque and angular velocity waveforms (rad) t=time (sec) T=1/f=period of oscillation of rotor and arm (sec) pi=3.14159 where: P-in-r=input power from each rotor motor (watts)

The mechanical efficiency in percent is expressed as:

where: Eff-mech=efficiency of mechanical power in instrument (%)

When the arm is used as the source of output power, it provides AC power at the oscillation frequency. The input power is supplied by a spindle motor and the rotor motors. The expression for the spindle motor is given by:

M-s=torque provided by spindle motor (N-m) Kt-s=torque constant for spindle motor (N-m/amp) Amp-s=current in spindle motor (amp) w-s=spindle rate (rad/sec) w-s′=spindle speed (rps) where: P-in-s=input power from spindle motor (watts)

The expression for the rotor motor power to oscillate the rotor is given by:

The input power supplied by the rotor motors to the arm is given by:

phi-r/a=phase angle between rotor torque and arm angular velocity waveforms (rad) where: P-r/a-max=amplitude of power supplied by rotor motor to arm (N-m/sec)

The input power supplied by centrifugal-forced torque to the arm is given by:

I-cent=constant relating spindle speed to centrifugal torque on half-arm (N-m-sec{circumflex over ( )}2) Theta-a=arm angle (rad) Theta-a-max=amplitude of arm oscillation (rad) where: P-cent-max=amplitude of power supplied centrifugal forces (N-m/sec)

The power required to oscillate the arm is given by:

MOI-a=moment of inertia of half arm (N-m-sec{circumflex over ( )}2) where: P-a-osc-max=power required to oscillate arm to Theta-a-max amplitude (watts)

The output power available from the oscillation of the arm is the difference between the total power being applied to the arm and the power required to oscillate the arm. The expression for the output power is given by the equations:

P-r/a-avg=contribution of power from rotor motor to oscillate arm (watts) P-cent-avg=contribution of power from centrifugal forces to oscillate arm (watts) P-a-osc-avg=power required to oscillate arm to Theta-a-max amplitude (watts) where: P-out=mechanical power available (watts)

The input power supplied by a spindle motor and the rotor motors is even by:

where: P-in=total input power supplied to operate instrument (watts)

The mechanical efficiency in percent is given by:

100 1 1 FIGS.A-C Table 1 below provides a list of the design parameters and calculated performance for a representative embodiment of the centrifugal gyroscopic deviceshown in.

TABLE 1 Calculated Performance and/or User Input (bold + Design Parameter underline) Units Notes General Device Parameters Rotor Inertia 1.20E−03 2 kg-m Rotor Radius 0.1 m Rotor Mass 0.12 kg 2 I = mrAssumes all mass is at radius, ignores motor. Rotor Arm Length 0.18 m Minimum of 2 × (Rotor Radius). Rotor Amplitude 12   deg Rotor Amplitude (Radians) 0.21 rad Spindle Frequency 4.17 Hz Spindle RPM 250    RPM Spindle Angular 26.20  rad/s Velocity (W) For Sinusoidal Motion Rotor Position Maximum 0.21 rad Max Rotor Angular Velocity (W) 5.49 rad/sec (Max Rotor Position) × (Spindle W). Max Rotor RPM 52    RPM Convert to RPM. Max Rotor Acceleration 144    2 rad/s (Max Rotor W) × (Spindle W). Max Rotor Torque 0.17 N-m Motor torque required. (Rotor Inertia) × (Max Rotor Acceleration). Rotor Angular Momentum (L)  0.0132 2 kg-m/ (2 × Angular Momentum) × (Rotor 2 sec W (both rotors)). Rotor Arm Arm Amplitude 3.6 degrees Max Arm Position 0.06 rad Amplitude converted to radians. Max Arm Angular Velocity (W) 1.65 rad/sec (Amplitude) × (Spindle W). Arm Acceleration 43.13  2 rad/sec (Max Arm W) × (Spindle W). Arm Inertia from 7.52E−03 2 kg-m Both rotors (2 m × (Rotor Arm Rotors 2 Length)) Torques Max Torque from Rotors 0.32 N-m Motor torque required to tilt the arm due to acceleration considering rotors only. Estimated Inertia 0.07 2 kg-m 4 kg at 0.1 m. Not Including Rotors Estimated Torque 3.02 N-m Not Including Rotors Max Total Torque 3.34 N-m Total motor torque required to tilt arm (not considering the torque that the rotors and spindle apply to the arm). Arm Moment of Inertia 0.08 2 kg-m Rotors plus estimate of rest of arm. Arm Angular Momentum 2.03 2 kg-m/ Angular momentum around spindle. 2 sec Centrifugal Forces Force at Horizontal 14.58  N 2 On one rotor m × w× r Torque from Both Rotors 2.58 N-m Force at horizontal times sin(2 * theta) from 2 * cos(theta) * sin(theta). Torque at 45 degrees. This torque is direction of rotor arm axis. This torque is in a direction to restore the arm to horizontal. Max Gyroscopic Torque 0.35 N-m (Rotor Angular Momentum) × on Arm (Spindle W). Max torque on arm from rotor momentum at horizontal. This torque opposes torque that the arm is applying to the rotor. Max Gyroscopic Torque 0.02 N-m (Rotor Angular Momentum) × (Arm on Spindle W). Max torque on spindle from rotor momentum due to arm movement. Powers Spindle Power 0.57 watts Max instantaneous power @600 RPM = (Gyroscopic torque) × (Spindle W due to arm movement). Rotor Arm Power 5.5 watts Max instantaneous rotor arm power = (Max motor torque required) × (Max Rotor Arm W) Rotor Power 0.95 watts Max instantaneous rotor power = (Max Rotor Torque) × (Max Rotor W) Other Performance Calculations Rotor Inertia Diameter 6.00E−04 2 kg-m Moment of inertia of rotor about diameter. Rotor Arm Torque 0.01 N-m Torque on rotor at max arm velocity. Rotor Spindle Torque 0.03 N-m Torque on rotor at spindle velocity. Centrifugal Force Rotor 15.22  N Thrust force on rotor motor. Rotor Acceleration Torque 0.03 N-m Torque on rotor shaft by rotor accelerating by the arm movement.

13 FIG.A 13 FIG.B 13 13 FIGS.A andB 13 13 FIGS.A,B 100 100 is a graph illustrating sample test results for the centrifugal gyroscopic devicehaving the characteristics described in Table 1 above showing the change in mechanical power of the spindle versus the amplitude of oscillation of the rotors. Table 2 below provides corresponding sample test results showing the change in mechanical power of the spindle versus the amplitude of oscillation of the rotors.is a graph illustrating sample test results for the centrifugal gyroscopic devicehaving the characteristics described in Table 1 showing the extraction of gyroscopic power from spindle rate harmonics. The data shown inwas computed from the measurement of two-cycle torque in the spindle using discrete Fourier transform (DFT) analysis. To produce the test results shown in, and Table 2, the pair of rotors were oscillated in synchrony with each other. The arm oscillated the rotors about an orthogonal axis. The oscillation of the arm was in synchrony with the rotor oscillation. The oscillations generated output gyroscopic torque about the spindle axis. In the testing, the gyroscopic torque was not large enough to overcome the large impediment torques on the spindle, thus requiring aid from the spindle motor. The rotating spindle feeds back gyroscopic and centrifugal torques to amplify the amplitude of arm oscillation. Spindle rate was adjusted for centrical resonance. The test data shows that for certain regions of operation mechanical power output can be greater than the input (e.g., with the rotor amplitude at 18 degrees, 27 degrees, or 36 degrees).

TABLE 2 Output Power Rotor Change in Gyroscopic Rotor Arm Total Minus Amplitude Spindle Power Power Power Power Input Power Input Power (Degrees) (Watts) (Watts) (Watts) (Watts) (Watts) (Watts)  9 0* 0** 0.22 −0.13 0.09 −0.09  (Reference (Gyroscopic power Value) value unknown) 18 −0.58 0.58 0.8 −0.49 0.31 0.27 27 −0.82 0.82 1.24 −0.87 0.37 0.45 36 −1.87 1.87 1.42 −1.22 0.2 1.67

14 14 FIGS.A-C 100 114 110 114 110 114 110 114 110 114 148 120 148 are graphs illustrating further sample test results for the centrifugal gyroscopic devicehaving the characteristics described in Table 1 above. During the testing, (i) the pair of rotors(“rotor”) were oscillated in synchrony with each other, (ii) the arm assembly(“arm”) oscillated the rotorsabout an orthogonal axis, and (iii) the oscillation of the arm assemblywas in synchrony with the oscillation of the rotors. Further, the arm assemblyand the rotorswere oscillated with the same amplitude and frequency and in phase with each other. The target position, load position, and current were recorded for the arm assembly, the rotors, and the controllers (e.g., the controller) for the first shaft(“spindle”). The target position was the position that the controllerwas programmed to attain, and the load position was the actual position of the motor at the time of the sample.

1 120 120 110 120 The oscillations generated output gyroscopic torque about the axis Aof the first shaft(e.g., the spindle). The rotating first shaftfed back gyroscopic and centrifugal torques to amplify the amplitude of oscillation of the arm assembly, and the rate of rotation of the first shaftwas adjusted for centrifugal resonance. Under some parameters, the mechanical power output appeared greater than the mechanical power input.

14 FIG.A 2 2 Referring to, the arm motor controller reported the current provided by the controller every 4 milliseconds. The average current (Amp) is the current samples averaged over an integer number of oscillation cycles in amperes. The fact that this current is negative means that arm is moving in the opposite direction as it normally moves for a current of this sign. The rms current (A) is the root-mean-square value of the recorded current. This number was used to calculate the IR power (watts). The average power (watts) is the torque (N-m) multiplied by the speed (rad/s). The torque was calculated from the current by multiplying the current by Kt which is the torque constant 0.34 N-m/Amp. In this graph, the average power is negative which means that the mechanical power out of the arm is more than the mechanical power (e.g., average current) that the motor controller puts into the arm. IR (watts) is the power dissipated in the windings of the motor. This is calculated from the rms current squared times the winding resistance.

14 FIG.B 2 Referring to, this graph shows data for one of the rotors at the same settings as the previous graph of arm measurements. The data for position and current were taken at 10 millisecond intervals by the rotor motor controller. The rotor ave cur (A) line is the average of the current measured by the rotor motor controller over an integral number of cycles of the oscillation frequency. The rms cur (A) line is the root-mean-square value of the rotor motor current. This was used to calculate the IR power that was dissipated in the resistance of the motor windings. The ave power (watts) line is the average of the torque times the velocity of the rotor averaged over an integral number of cycles of the oscillation frequency. The torque was calculated from the current by multiplying the current in amperes by the torque constant of the motor Kt which is 0.06 N/Amp for the rotor motors.

14 FIG.C 2 Referring to, the spindle motor controller logged position and current at 4 milliseconds per sample. The ave cur (A) line is the average of the current over an integral number of cycles of the oscillation frequency. The rms cur (A) line is the root-mean-square of the current. Since the spindle current was always in the same direction, the rms and the average are very close to each other. The ave pwr (watts) line is the torque times the speed of the spindle. The torque is calculated from the current by multiplying the current by Kt which is 0.34 N-m/amp. The IR pwr (watts) is the power dissipated in the resistance of the windings of the motor.

Notably, the power required of the spindle motor decreased as the amplitude of the oscillation increased. The arm motor also showed a decrease. The rotor motors showed an increase that may, but not necessarily, offset this decrease. If the decrease in spindle power with increasing amplitude is further confirmed, then this can be seen as evidence that the oscillation of the arm and rotors results in power being added to the spindle.

15 15 FIGS.A-D 114 120 100 are graphs illustrating sample test results for the effects of oscillation of the rotorson movement of the arm assemblyof the centrifugal gyroscopic device. These effects were studied under two different conditions. First, the arm was held in a position with the motor controller while the rotor was oscillated. The current drawn by the arm motor was used to calculate the torque on the arm. In the second method, the arm motor controller was loaded with code which had the PID gains all set to zero. This allowed the position and current data to be recorded but the controller did not react to the position. The current in this case is the current generated by the motor when it moved under the influence of the rotor motions.

15 FIG.A Referring to, this graph shows the arm being held in position by the arm motor. During testing, the position varied only a small amount (+−0.3 degrees) and the speed was nearly zero. This is the torque calculated from the current by multiplying the current by Kt (0.34 N-m/amp). The data shows a gyroscopic torque being applied to the arm due to the oscillation of the rotor combined with the rotation of the spindle.

15 FIG.B Referring to, in this case the arm was left free to move and the arm motor controller was loaded with PID gains of zero so that the motion and current could be recorded. This graph shows the arm being oscillated by the influence of the rotor oscillations and spindle rotation.

15 FIG.C Referring to, the torque applied to the arm was calculated from the current in the arm by multiplying by Kt (0.34 N-m/Amp) of the arm motor.

15 FIG.D Referring to, this graph shows a plot of torque versus speed to illustrate whether the device is consuming power or producing power. If the signs of the torque and the speed are the same, the motor is transferring power to the device. If the signs are different, then the device is transferring power to the motor. In the case of the controllers, this transfer of power to the motor may have been wasted by producing heat. In this case the speed and torque have opposite signs, implying that the arm motor is not transferring energy to the device.

16 16 FIGS.A-F 120 114 100 are graphs illustrating sample test results for the effects of oscillation of the arm assemblyon the torque of the rotorsof the centrifugal gyroscopic device. When the data was collected for the effect of the rotor on the arm motions, the position and current data for the rotor was also collected. This data was collected to determine if the rotors were supplying energy to the arm.

16 FIG.A Referring to, the data in this graph shows one of the rotors oscillating between 0 and 72 degrees. The actual position was arbitrary and was an artifact of the algorithm for generating the oscillation. The oscillation of the rotor can be considered to be oscillating +/−36 degrees. The actual oscillation amplitude is slightly larger than this and the phase lags a little from the programmed target position. In this case, the arm was held in a nearly fixed position while the rotor oscillated, and the spindle rotated.

16 FIG.B Referring to, the rotor amplitude decreased when the arm was free to move compared to when the arm was held in position by the arm motor. This could be due to some energy being transferred from the rotor to the arm.

16 FIG.C Referring to, this graph shows current and speed data for the rotor with the arm held in position.

16 FIG.D Referring to, this graph shows the current and speed in the rotor with the arm free to move. The current in the arm was less when the arm is free to move. The graph of torque versus speed shows whether the rotor motor is transferring energy to the device or if the device is transferring energy to the motor. When the signs are the same, the motor is transferring energy to the device. When the signs are opposite, the transfer is the other way.

16 FIG.E Referring to, in the case where the arm was held in position by the arm motor, the resulting motion was an ellipse with an equal amount of energy transferred in both directions.

16 FIG.F Referring to, in the case where the arm was free to move, this graph is tilted to put more points in the two quadrants where the signs of the speed and torque are the same. This indicates that more energy is being transferred from the rotor motor to the rotor than is being transferred from the rotor to the motor. This is evidence that the rotor motor is providing energy to the arm motion. Notably, the amplitude of the current oscillation is not the factor that determines the amount of power transferred, but the relative phase of the torque and speed curves, which is confirmed by the fact that the amplitude of the current oscillation was greater in the case when there was little energy transfer from the motor and the amplitude of the current oscillation was smaller in the case when the transfer of energy from the motor to the rotor was greater.

Table 3 below provides representative characteristics and/or operational parameters of various elements of the centrifugal gyroscopic devices described herein.

TABLE 3 Representative Element of a Centrifugal Gyroscopic Embodiments of the Present Device in Accordance with Representative Characteristics and/or Operational Technology Parameters Rotors (e.g., Pivotable Movement: +/− 20 degrees at 15 Hertz. Rotors 114) 2 Inertia: 12,112.5 grams × cm(+/−1%). Geometry: balanced/symmetric around its axis of rotation with majority of mass at outer ring. Position on Rotor Arm: rotors positioned at a distance at least 2× the radius of the rotor from the center of the rotor arm. Average Input Power: 97 watts. Peak Input Power: 195 watts. Rotor Mass: mass of the rotor minimized to increase the rotor arm inertia, and forces on the rotor axis gearbox. E.g., 260 grams. Rotor Diameter: diameter of the rotor impacts the length of the rotor arm due to the requirement of distance from rotor arm center as set forth above. In an example configuration, the motors to generate the rotor motion are straight-line coupled to the rotors. They are also kept toward the center of the arm to reduce rotor arm inertia. Rotor Motor: Kollmorgen BLDC motor modeled in example as: AKM2G-33PL (48 VDC)/Low Voltage DC Drive with a 5:1 gearbox. Rotor Gearbox Axial Force: If the spindle is turning at 900 rpm, the rotor is at radius 25.66, traveling 54 mph, and pulling outward with 133 lb-f or 593 Newton. In this example configuration the rotor is mounted directly to a gearbox, the bearings of the gearbox would be subjected to that axial force. Rotor Gearbox Radial Force: The rotor arm can accelerate/sweep through 21.5 degrees in 0.0166 second. The rotor can be 25.7 centimeters from the center of the rotor arm. The chord length is about 0.096 meter. Assuming a triangular acceleration profile, the acceleration of the rotor is 691.2 meters per second squared, causing a 180 Newton force on the rotor. The distance from the gearbox flange to the rotor center plane can be 5 mm, such that the gearbox tilting torque is 180N × 0.005M = 0.9 N-Meter. Rotor Drive Centrifugal Force: An example of the forces generated by the motor gearbox combination: Total Mass: 2300 gram/5.07 lb (1400 grams motor, 900 grams gearbox). Center of Mass: 13.46 cm from center of arm. Spinning at 900 RPM the motor/gearbox will pull on the coupling tube with 618.2 lb-f/ 2750 Newton. Combined with the rotor pull force of (133 lb-f or 593 Newton) results in 751.2 lb-f 3,343 Newton at each end of center coupler. Rotor Arm Pivotable Movement: +/−43 degrees at 15 Hertz. (e.g., Arm Rotor Arm Motor: Assembly 110) Rotor Arm Assist Mode: AKM2G-44NL (96 VDC)/Low Voltage DC Drive with a 3.2:1 gearbox. Rotor Arm Start Mode: AKM2G-44NL (96 VDC)/Low Voltage DC Drive with a 12:1 gearbox. Average Input Power: 524 watts. Peak Input Power: 1050 watts. Spindle Shaft Rotation: 15 revolutions per second or 900 rotations per (e.g., Spindle minute (RPM). 120) Mass: 33,504 grams/74 pounds. 2 Inertia about “Z” axis: 17,128,266 grams × cm. Spindle Arm: AKM2G-31ML (96 VDC)/Low Voltage DC Drive with an 8:1 gearbox. Average Input Power: 16 watts. Peak Input Power: 125 watts. Power Source The device power will not require 3-phase, not need more (e.g., Power than 240 VAC split phase, can operate off standard 120 VAC Source 142) 10-15 Amp residential AC outlet. Regeneration Predominantly the motion considered is accelerating and decelerating cyclically. To provide maximum efficiency, energy can be captured during braking/decelerating in capacitors on DC Bus that will provide energy for harvest on next acceleration move. Rotor Regeneration: Rotor Peak Velocity: 400 RPM. 2 Rotor Inertia: 12,112.5 gram × cm∥ 0.00121125 2 KgM. Braking Joules: 1.0626 J. decelerating cyclically. Rotor Arm Regeneration: Rotor arm Peak Velocity: 428 RPM. 2 Inertia handled by motor: 59,556 gram × cm∥ 2 0.00596 KgM. Braking Joules: 5.986 J. Total Regeneration: For a total of ~14 Joules (Watt-Seconds) to be captured in ¼ cycle (1/60) so average of about 845 watts for 0.0167 seconds.

The following examples are illustrative of several embodiments of the present technology:

a shaft rotatable about a first axis; an arm coupled to the shaft and configured to rotate with the shaft, wherein the arm is pivotable about a second axis different from the first axis; at least one rotor coupled to the arm and configured to pivot with the arm about the second axis, wherein the at least one rotor is further pivotable about a third axis different from the first axis and different from the second axis; and a control system operably coupled to at least one of the shaft, the arm, and the at least one rotor, wherein the control system is configured to bring the shaft, the arm, and the at least one rotor into at least approximately a resonant mode of operation in which (a) the shaft rotates about the first axis at a rotational rate, (b) the arm oscillates about the second axis at a first frequency, and (c) the at least one rotor oscillates about the third axis at a second frequency at least approximately equal to the first frequency. 1. A centrifugal gyroscopic device, comprising:

2. The centrifugal gyroscopic device of example 1 wherein the first frequency and the second frequency are at least approximately equal to the rotational rate.

3. The device of example 1 or example 2 wherein the control system includes a motor assembly positioned to drive the at least one rotor to oscillate about the third axis at the second frequency.

4. The device of any one of examples 1-3 wherein the oscillation of the arm and the oscillation of the at least one rotor generate a gyroscopic torque which acts to rotate the shaft about the first axis, and wherein the gyroscopic torque is substantially maximized in the resonant mode of operation.

5. The device of example 4 wherein the control system is configured to change a phase relationship between the first frequency of the arm and the second frequency of the at least one rotor to change an average value of the gyroscopic torque.

6. The device of example 4 or example 5 wherein the control system further includes a motor assembly positioned to drive the arm to oscillate about the second axis at the first frequency.

7. The device of example 6 wherein the control system is configured to control the motor assembly to change a phase relationship between the first frequency of the arm and the second frequency of the at least one rotor to change an average value of the gyroscopic torque.

8. The device of any one of examples 1-7 wherein the rotation of the arm generates a centrifugal force that acts to oscillate the arm about the second axis.

9. The device of any one of examples 1-8, further comprising a power generator coupled to the shaft and configured to generate an output power from the rotation of the shaft.

10. The device of any one of examples 1-9, further comprising a power generator coupled to the arm and configured to generate an output power from the pivotable motion of the arm.

11. The device of any one of examples 1-10 wherein the second axis is orthogonal to the first axis.

12. The device of any one of examples 1-11 wherein the third axis is orthogonal to the second axis.

13. The device of any one of examples 1-12 wherein the at least one rotor includes a first rotor coupled to a first end portion of the arm and a second rotor coupled to a second end portion the arm.

pivoting an arm of the centrifugal gyroscopic device about a second axis different from the first axis, wherein the arm is pivotably coupled to the shaft and configured to rotate with the shaft; pivoting at least one rotor of the centrifugal gyroscopic device about a third axis different from the first axis and different from the second axis, wherein the at least one rotor is pivotably coupled to the arm and configured to pivot with the arm about the second axis; and controlling the rotation of the shaft, the pivoting of the arm, and/or the pivoting of the at least one rotor to bring the shaft, the arm, and the at least one rotor into a resonant mode of operation in which (a) the shaft rotates at a rotational rate, (b) the arm oscillates about the second axis at a first frequency, and (c) the at least one rotor oscillates about the third axis at a second frequency at least approximately equal to the first frequency. 14. A method of operating a centrifugal gyroscopic device, the method comprising: rotating a shaft of the centrifugal gyroscopic device about a first axis;

15. The method of example 14 wherein the first frequency and the second frequency are at least approximately equal to the rotational rate.

16. The method of example 14 or example 15 wherein the method further comprises generating a gyroscopic torque by the oscillation of the arm and the oscillation of the at least one rotor which acts to rotate the shaft about the first axis.

17. The method of example 16 wherein the method further comprises changing a phase relationship between the first frequency of the arm and the second frequency of the at least one rotor to change an average value of the gyroscopic torque.

18. The method of any one of examples 14-17 wherein the method further comprises generating power, with a power generator coupled to the shaft, by the rotating the shaft.

19. The method of any one of examples 14-18 wherein the second axis is orthogonal to the first axis, and wherein the third axis is orthogonal to the second axis.

a spindle rotatable about a first axis; an arm coupled to the spindle and configured to rotate with the spindle, wherein the arm has a first end portion and a second end portion, and wherein the arm is pivotable about a second axis different from the first axis; a first rotor coupled to the first end portion of the arm; a second rotor coupled to the second end portion of the arm, wherein the first rotor and the second rotor are each pivotable about a third axis different from the first axis and different from the second axis; and a control system operably coupled to at least one of the shaft, the arm, the first rotor, and the second rotor, wherein the control system is configured to bring the shaft, the arm, the first rotor, and the second rotor into a resonant mode of operation in which (a) the shaft rotates at a rotational rate, (b) the arm oscillates about the second axis at a first frequency at least approximately equal to the rotational rate, and (c) the first rotor and the second rotor oscillate about the third axis at a second frequency at least approximately equal to the first frequency. 20. A centrifugal gyroscopic device, comprising:

The above detailed description of embodiments of the present technology are not intended to be exhaustive or to limit the technology to the precise forms disclosed above. Although specific embodiments of, and examples for, the technology are described above for illustrative purposes, various equivalent modifications are possible within the scope of the technology as those skilled in the relevant art will recognize. For example, although steps are presented in a given order, other embodiments may perform steps in a different order. The various embodiments described herein may also be combined to provide further embodiments.

From the foregoing, it will be appreciated that specific embodiments of the technology have been described herein for purposes of illustration, but well-known structures and functions have not been shown or described in detail to avoid unnecessarily obscuring the description of the embodiments of the technology. Where the context permits, singular or plural terms may also include the plural or singular term, respectively.

As used herein, the terms “about,” “approximately,” “generally”, “substantially,” and the like refer to values within 10% of the stated value. As used herein, the phrase “and/or” as in “A and/or B” refers to A alone, B alone, and A and B. To the extent any materials incorporated herein by reference conflict with the present disclosure, the present disclosure controls. Additionally, the term “comprising” is used throughout to mean including at least the recited feature(s) such that any greater number of the same feature and/or additional types of other features are not precluded. It will also be appreciated that specific embodiments have been described herein for purposes of illustration, but that various modifications may be made without deviating from the technology. Further, while advantages associated with some embodiments of the technology have been described in the context of those embodiments, other embodiments may also exhibit such advantages, and not all embodiments need necessarily exhibit such advantages to fall within the scope of the technology. Accordingly, the disclosure and associated technology can encompass other embodiments not expressly shown or described herein.